[GAP Forum] Question about Representation of Permutation group's elements

[Marco Costantini]

Dear Kang ByoungKwan,

> I am a beginner of GAP.

Welcome!

> If I want to calculate some math problems related to all elements of
> permutation group,
> how can I represent the elements of permutation group in GAP?

A permutation is represented like

(1,3,4,2,5)

The group generated by (1,2,3) and (1,4,5) is represented by

Group( (1,2,3), (1,4,5) )

(remember ';' at the end of the command)

> For example, there are S_5. I want to computing some equation related to
> group elements. How can I take all elements of S_5 in GAP for using
> computing ?

See the help giving the command

?Basic Groups

In general, it may be not efficient to list all the elements of a Group. It
may be better to look at the conjugacy classes: try

ConjugacyClasses( SymmetricGroup( 5 ) );

All the best,
Marco Costantini